Higher-order Spectral Filtering Effects on the Evolution of Stationary Dissipative Solitons

Abstract

A semianalytical method to study the effects of the higher-order spectral filtering in the cubic-quintic complex Swift-Hohenberg equation (CSHE) through the dynamics of one soliton was applied. The approach is based on a reduction from an infinite-dimensional dynamical dissipative system to a finite-dimensional model. This formulation is helpful to study the ground state of the soliton dynamic since it depends on a trial function and a good set of parameters. With real coefficients, the CSHE exhibits stationary dissipative solitons in space with the equation parameters, and the higher-order spectral filtering has a real impact on the cartographies of stationary soliton domain. The detailed analysis reveals the effects of spectral filtering term on the stationary soliton parameters, and displays that it differently influences the cubic and quintic terms of the CSHE. The results highlight the major influence of the spectral filtering on the temporal width of the stationary soliton whereas it does not have a real impact on the amplitude and the spatial width.